查询词典 compact convergence

Since a new generalized projection technique is contained in the auxiliary direction formula, under some mild assumptions without the strict complementarity, the global convergence and superlinear convergence of the algorithm can be obtained.

由于一种新的广义投影技术包含在辅助方向的计算公式中，因而在无严格互补等较温和的假设下便可得到算法的全局收敛性及超线性收敛性。

LC1 unconstrained optimization problem was discussed in the second chapter, giving a new trust region method and proving its global convergence and superlinear convergence under some mild conditions .

第二章讨论了LC~1无约束优化问题。给出了一个新的信赖域算法，并在一定的条件下证明了算法的全局收敛性和局部超线性收敛性。

To solve it, we turn it into nonsmooth equations, utilizing inexact theory we give an inexact generalized Newtons method and under some mild conditions we prove that it is global convergence and superlinear convergence .

首先将其约束问题的求解转化为非光滑方程组的求解，然后利用不完全求解理论给出了一个非精确的广义牛顿算法，在一定的条件下证明了算法的全局收敛性和局部超线性收敛性并给出了LC~1非线性约束问题的收敛性条件。

We also introduce a control function, prove the global convergence, and prove the local superlinear convergence under some conditions. Then we propose another new algorithm by using an existed approximation functions, which has the same characters as the first algorithms does. Finally, the result of the numerical experiments indicates the efficiency of the first algorithm. The paper contains four parts.

本文还引入了新的控制函数，并证明了算法具有全局收敛性和在一定的条件下具有局部超线性收敛性；然后，在第一个算法的基础上，本文利用已有的光滑逼近函数提出了另外一个新的算法，通过适当参数选取，证明了新的算法具有与第一个算法同样良好的收敛性质；最后，通过数值计算说明了算法的高效性。

In Chapter 3, we propose two new quasi-Newton type trust region methods for solving unconstrained optimization problems. These algorithms combine two types of the preconvex part of modified Broydens family proposed in chapter 1 with trust region algorithm effectively, they have global convergence property and superlinear convergence rate.

第三章，给出了用来求解无约束最优化问题两种新的拟牛顿信赖域算法，这些算法将第一章给出的两种修改Broyden非凸族与信赖域算法有效结合起来，它们具有全局收敛性和超线性收敛速度。

Which possesses global convergence and locally superlinear convergence proven without strict complementarity at the Danskin point.

在不假设在Danskin点处满足严格互补条件的情况下证明了算法具有超线性收敛速度及全局收敛的性质。

Chapter 6 is contributed to studying the convergence properties of pariwise NQD random sequences. We extend the Kolomogrov-type inequality, Baum and Katz complete convergence, the three series theorem, Marcinkiewicz strong law of large number and Jamison theorem.

第六章研究两两NQD列的收敛性质，首先给出两两NQD列的Kolmogorov型不等式，进而讨论它的若干收敛性质，获得了与独立情形一样的Baum和Katz完全收敛定理；几乎达到独立情形著名的Marcinkiewicz强大数定律，三级数定理，推广了著名的Jamison定理。

In order to make the new recursive method convergence fast, the RLS-like forgetting factor is introduced to construct the new data Hankel matrices. In the framework of subspace methods, the gradient type subspace tracking method is used to implement the update of the state subspace, which results the unbiased estimate. Different from traditional offline method, the system matrices are recursively computed using RLS method. The convergence analysis of the proposed method is given and finally, the efficiency of this method is illustrated with a simulation example.A new closed-loop identification method is proposed to implement consistency estimation of closed-loop subspace identification.

引入RLS-like遗忘因子机制构造新的数据矩阵，更好地跟踪系统时变信息，提高递推算法的收敛速度；在子空间辨识框架内，采用梯度型子空间跟踪算法实现对状态子空间的更新，避免了子空间近似带来的估计有偏性；与传统的离线算法不同，在得到系统状态子空间后，基于递推最小二乘方法提出新的算法，实现对系统矩阵的递推估计；并给出递推子空间辨识算法的收敛性分析；最后通过仿真实例验证算法的有效性。

The main conclusion is that no remarkable σ convergence and unconditional β convergence exist in the...

论文基本结论表明，整个转型期中国农业TFP增长并不存在显著的σ收敛和绝对β收敛性，但存在显著的条件β收敛性。

The main contents are as follows.1 For the state control problem in closed quantum systems, according to the distance between states, the error between states and the average value of an imaginary mechanical quantity, three Lyapunov functions are chosen, respectively. The corresponding control law designs and the convergence analyses are studied. Especially, for the Lyapunov function based on the distance between states, a class of control laws that can solve the problem that an initial state is orthogonal to a goal state is designed. The convergence of the system is analyzed via LaSalle\'s principle and one method to find the largest invariant set of the closed loop system is proposed by linearizing the unitary evolution operator at the corresponding instants.

在这一背景下，本论文在指出研究量子系统控制的必要性、回顾量子系统控制理论和方法的研究现状的基础上，从控制理论的角度研究Lyapunov理论和最优控制理论对于封闭量子系统的应用以及开放系统中的若干问题，主要内容包含以下几个方面。1针对封闭量子系统中的状态控制问题，根据状态间的距离、状态间的偏差、一个虚拟力学量的均值，分别选择三种Lyapunov函数进行相应的控制律设计和收敛性分析。

There are different types of personal loans available.

有许多不同类型的个人贷款优惠。

The above mentioned teaching model of spiral rising can be used to avoid rigidness in teaching.

上述螺旋式上升的教学模式，可以避免教学形成模式後的僵化现象。